NMR spectroscopy is a relatively insensitive technique and many biomolecular applications operate near the limits of sensitivity and resolution. A particularly challenging example is detection of the quadrupolar nucleus 17O, due to its low natural abundance, large quadrupole couplings, and low gyromagnetic ratio. Yet the chemical shift of 17O spans almost 1000 ppm in organic molecules and it serves as a potentially unique reporter of hydrogen bonding in peptides, nucleic acids, and water, and as a valuable complement to 13C and 15N NMR. Recent developments including the multiple-quantum magic-angle spinning (MQMAS) experiment have enabled the detection of 17O in biological solids, but very long data acquisitions are required to achieve sufficient sensitivity and resolution. Here, we perform nonlinear sampling in the indirect dimension of MQMAS experiments to substantially reduce the total acquisition time and improve sensitivity and resolution. Nonlinear sampling prevents the use of the discrete Fourier transform; instead, we employ maximum entropy (MaxEnt) reconstruction. Nonlinearly sampled MQMAS spectra are shown to provide high resolution and sensitivity in several systems, including lithium sulfate monohydrate (LiSO4-H217O) and -asparagine monohydrate (H217O). The combination of nonlinear sampling and MaxEnt reconstruction promises to make the application of 17O MQMAS practical in a wider range of biological systems.